   # Architecture, a floor plan of a museum is shown. Draw a graph that represents the floor plan, where each vertex represents a room and an edge connects two vertices if there is a doorway between the two rooms. Is it possible to walk through the museum and pass through each doorway without going through any doorway twice? Does it depend on whether you return to the room you started at? Justify your conclusion. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.1, Problem 29ES
Textbook Problem
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## Architecture, a floor plan of a museum is shown. Draw a graph that represents the floor plan, where each vertex represents a room and an edge connects two vertices if there is a doorway between the two rooms. Is it possible to walk through the museum and pass through each doorway without going through any doorway twice? Does it depend on whether you return to the room you started at? Justify your conclusion. .
To determine

To graph the floor plan. To determine if it is possible to walk through the museum and pass through each doorway without going through any doorway twice. To check if it depends on whether the ending point is same as the starting point.

### Explanation of Solution

Given information:

Given, a floor plan of a museum is shown below, in whose graph each room is represented by a vertex and a doorway between the two rooms is represented by an edge.

Calculation:

To make the graph, the rooms are labelled first as per the given information.

Using the above image, the graph can be made as:

It is possible to walk through the museum and pass through each doorway without going through any doorway twice if the graph satisfies the condition of either Euler circuit or Euler path.

An Eulerian graph (that starts and ends at the same vertex) is said to be Euler circuit if it uses every edge, but only once. (i.e. no edge is used more than once).

Euler path is defined as the path in a connected graph that has exactly two vertices of odd degree with all the remaining vertices of even degree and the path starts at one of the vertices with odd degree and ends at the other vertex with odd degree...

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